Write 2014 with the first four prime numbers, with the
aid of the operations addition, multiplication and exponentiation.

Problems

Grades: 6th to 8th, 3rd to 5th

Expression/Equation

Algebraic Thinking

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Multiply and divide within 100.

3.OA.C.7, 4.OA.B.4, 6.EE.A.1

On the map shown, begin at Start. Travel the roads along any path you
like, following typical traffic laws, and each time you pass a number,
add it to your current sum. However, you are not allowed to pass any
number more than once. Can you reach End with a sum of 91?

Problems

Grades: 3rd to 5th

Num & Ops Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.A.2, 4.NBT.B.4

A magic rectangle is an *m*× *n* array of the positive integers from 1 to *m*× *n* such
that the numbers in each row have a constant sum and the numbers in
each column have a constant sum (although the row sum need not equal the
column sum). Shown below is a 3 × 5 magic rectangle with the integers
1-15.

Two of three arrays at left can be filled with the integers 1-24 to form a magic rectangle. Which one can't, and why not?

Problems

Let A = 1, B = 2, and so on, with each letter equal to its position in the alphabet. The *lexivalue* of a word is the sum of the values of its letters. For example, ROMANS has a lexivalue of 18 + 15 + 13 + 1 + 14 + 19 = 80.

Now, do the following:

- Pick a number.
- Convert it into its representation in Roman numerals.
- Find the lexivalue for that Roman numeral.

For example, if you choose 11, that becomes XI in Roman numerals, and XI has a lexivalue of 24 + 9 = 33.

Are there any numbers for which the lexivalue is equal to the original number?

Problems

A figure resembling a spiral is shown with 35 matches. Move 4 matches to form 3 squares.

Problems

Grades: 6th to 8th

Geometry

Draw construct, and describe geometrical figures and describe the relationships between them.

7.G.A.2